/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 17 Solve each equation. Check each ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 17

Solve each equation. Check each solution. See Examples 7 and 8 . \(2 x-4=16\)

Short Answer

Expert verified
The solution is \(x = 10\).

Step by step solution

01

Isolate the Variable

Begin by adding 4 to both sides of the equation to get the variable term by itself:\[2x - 4 + 4 = 16 + 4\]This simplifies to:\[2x = 20\]
02

Solve for x

Now divide both sides of the equation by 2 to solve for \(x\):\[\frac{2x}{2} = \frac{20}{2}\]This simplifies to:\[x = 10\]
03

Check the Solution

Substitute \(x = 10\) back into the original equation to verify:\[2(10) - 4 = 16\]Calculate:\[20 - 4 = 16\]Since the left side of the equation equals the right side, the solution \(x = 10\) is correct.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solving Equations
When faced with a linear equation like \(2x - 4 = 16\), the primary goal is to find the value of \(x\) that makes the equation true. In mathematics, this process is known as solving an equation. To solve an equation means to find all values of the variable that satisfy the equation. This often involves a series of steps to manipulate the equation and isolate the variable. By understanding the structure of linear equations, you can apply strategies like combining like terms, using inverse operations, and simplifying expressions to efficiently solve the equation. Here are some general steps for solving linear equations:
  • Identify the equation to be solved.
  • Use inverse operations to simplify the equation.
  • Rearrange the equation to isolate the variable.
  • Perform any necessary arithmetic to find the variable's value.
      • Each step fits into a larger methodical process, helping to systematically solve and verify solutions.
Isolation of Variable
Isolation of the variable is crucial in solving equations, as it helps simplify the process by focusing only on the variable in question. In our example, the equation \(2x - 4 = 16\) requires isolating the variable \(x\). This involves rearranging the equation so that \(x\) stands alone on one side of the equation.The process can be broken down into smaller steps:
  • Identify and eliminate any constants or coefficients that are attached to the variable.
  • Use inverse operations to move these numbers to the other side of the equation.
  • Simplify the equation step-by-step until the variable is isolated.
For instance, adding \(4\) to both sides eliminates the \(-4\) and using division by \(2\) takes care of the coefficient of \(x\). This leaves \(x\) by itself, allowing us to plainly see its value.
Checking Solutions
Once a potential solution is obtained, it's important to verify it. This ensures that your solution is not only reasonable but correct. In mathematics, checking solutions involves substituting the found value back into the original equation to ensure both sides remain equal.Consider our earlier example with the solution \(x = 10\):
  • Substitute \(x = 10\) back into the original equation \(2x - 4 = 16\).
  • Calculate the left-hand side: \(2(10) - 4\) which simplifies to \(20 - 4\).
  • Verify equality by ensuring the result \(16\) matches the right-hand side of the equation.
The equality of both sides confirms the solution is accurate. Checking solutions is a crucial final step in solving equations, reinforcing the correctness and reliability of the answer.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Fill in the box with \(<,>, \leq,\) or \(\geq\). See the Concept Check in this section. If \(m \leq n,\) then \(-2 m \square-2 n\)

Evaluate each expression. $$ 3^{4} $$

The room numbers of two adjacent classrooms are two consecutive even numbers. If their sum is 654 , find the classroom numbers.

Evaluate each expression for the given values. See Section 1.8 \(\frac{1}{2} B h ; \quad B=14\) and \(h=22\)

Dr. Dorothy Smith gave the students in her geometry class at the University of New Orleans the following question. Is it possible to construct a triangle such that the second angle of the triangle has a measure that is twice the measure of the first angle and the measure of the third angle is 5 times the measure of the first? If so, find the measure of each angle. (Hint: Recall that the sum of the measures of the angles of a triangle is \(180^{\circ} .\) )
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.